Problem: What is the measure, in units, of the hypotenuse of a right triangle with leg lengths of 75 and 100 units?
Using the Pythagorean Theorem, \begin{align*} d&=\sqrt{75^2+100^2} \\ &=\sqrt{25^2(3^2+4^2)} \\ &=25\sqrt{3^2+4^2} \\ &=25\sqrt{9+16} \\ &=25\sqrt{25} \\ &=25 \cdot 5 \\ &=\boxed{125} \text{units} \end{align*}